''Quantum'' Rational Numbers
Research Director
Valentin Ovsienko introduces a novel q-deformed cross-ratio, connecting classical geometry, combinatorics, and mathematical physics through the lens of 'quantum' rational numbers.
The classical cross-ratio "crosses" both classical and modern mathematics, linking geometry with combinatorics, dynamics, and mathematical physics. It provides natural coordinates on many moduli spaces. In this talk, I will introduce a new q-deformed, or ``quantum'' cross-ratio: a PSL(2,Z)-invariant of ordered quadruples of distinct points on the rational projective line. The construction is based on the theory of q-deformed rational numbers developed jointly with Sophie Morier-Genoud. I will discuss several properties of this new invariant, with its close connection to q-deformed Coxeter frieze patterns taking centre stage.
Valentin Ovsienko (CNRS - Université de Reims Champagne-Ardenne)
Seminar notes & discussion
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